Rainbow Mind Map: Refraction of Light

Laws of Refraction

• Snell's Law: n₁sinθ₁ = n₂sinθ₂
• Incident, refracted ray and normal lie in same plane
• Ratio of sine of angles is constant
• Experimental verification using glass slab

Snell's Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media.

Experimental Verification: Using a glass slab and pins, we can verify that:

• The incident, refracted ray and normal all lie in the same plane
• The ratio sin i / sin r is constant for a given pair of media

Refraction & Speed

• Refractive index n = c/v
• Light slows down in denser medium
• Lateral displacement
• Principle of reversibility

Refractive Index: n = speed of light in vacuum (c) / speed in medium (v). Higher n means slower light speed.

Lateral Displacement: The perpendicular shift of light ray when passing through a parallel-sided slab.

Principle of Reversibility: The path of light is reversible - if direction is reversed, light will follow the same path.

Depth & Effects

• Real vs apparent depth
• Apparent depth = Real depth / n
• Twinkling of stars
• Mirage formation

Apparent Depth: When viewing from air into water, objects appear 3/4 of their actual depth (for water, n=4/3).

Twinkling of Stars: Caused by atmospheric refraction as starlight passes through layers of different refractive indices.

Mirage: Caused by total internal reflection in air layers of different temperatures (and thus different refractive indices).

Total Internal Reflection

• Critical angle θc = sin⁻¹(n₂/n₁)
• Optical fibers
• Prisms in binoculars
• Diamonds sparkle

Critical Angle: θc = sin⁻¹(n₂/n₁) where n₁ > n₂. For glass to air, θc ≈ 42°.

Applications:

• Optical Fibers: Use TIR to transmit light signals with minimal loss
• Prisms: Used in binoculars to reflect light through 90°
• Diamonds: Cut to maximize TIR, creating sparkle

Prism Refraction

• Angle of deviation
• Minimum deviation
• Dispersion of light
• Rainbow formation

Deviation by Prism: δ = i + e - A, where A is prism angle.

Minimum Deviation: Occurs when i = e, giving δmin = 2i - A.

Dispersion: Different wavelengths refract differently, creating spectrum (n varies with λ).

Rainbow: Caused by dispersion, refraction and TIR in water droplets.

Lenses & Imaging

• Convex (converging) lens
• Concave (diverging) lens
• Lens formula: 1/f = 1/v - 1/u
• Magnification

Convex Lens: Thicker at center, converges parallel rays to focus.

Concave Lens: Thinner at center, diverges parallel rays.

Lens Formula: 1/f = 1/v - 1/u where f=focal length, v=image distance, u=object distance.

Magnification: m = v/u = height of image/height of object.

Applications

• Simple microscope
• Power of lens (diopters)
• Focal length determination
• Corrective lenses

Simple Microscope: Uses convex lens for magnification M = 1 + D/f where D=least distance of distinct vision (25cm).

Lens Power: P = 1/f (in meters), measured in diopters (D).

Focal Length: Can be determined using lens formula or plane mirror method.

Corrective Lenses: Convex for hypermetropia, concave for myopia.

Interactive Rainbow Mind Map on Refraction of Light | The Physics Next